Geometric {stats} | R Documentation |
Density, distribution function, quantile function and random
generation for the geometric distribution with parameter prob
.
dgeom(x, prob, log = FALSE) pgeom(q, prob, lower.tail = TRUE, log.p = FALSE) qgeom(p, prob, lower.tail = TRUE, log.p = FALSE) rgeom(n, prob)
x, q |
vector of quantiles representing the number of failures in a sequence of Bernoulli trials before success occurs. |
p |
vector of probabilities. |
n |
number of observations. If |
prob |
probability of success in each trial. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x]. |
The geometric distribution with prob
= p has density
p(x) = p (1-p)^x
for x = 0, 1, 2, …, 0 < p ≤ 1.
If an element of x
is not integer, the result of dgeom
is zero, with a warning.
The quantile is defined as the smallest value x such that F(x) ≥ p, where F is the distribution function.
dgeom
gives the density,
pgeom
gives the distribution function,
qgeom
gives the quantile function, and
rgeom
generates random deviates.
Invalid prob
will result in return value NaN
, with a warning.
The length of the result is determined by n
for
rgeom
, and is the maximum of the lengths of the
numerical parameters for the other functions.
The numerical parameters other than n
are recycled to the
length of the result. Only the first elements of the logical
parameters are used.
dgeom
computes via dbinom
, using code contributed by
Catherine Loader (see dbinom
).
pgeom
and qgeom
are based on the closed-form formulae.
rgeom
uses the derivation as an exponential mixture of Poissons, see
Devroye, L. (1986) Non-Uniform Random Variate Generation. Springer-Verlag, New York. Page 480.
Distributions for other standard distributions, including
dnbinom
for the negative binomial which generalizes
the geometric distribution.
qgeom((1:9)/10, prob = .2) Ni <- rgeom(20, prob = 1/4); table(factor(Ni, 0:max(Ni)))